-
作者：Xu, Mengyu; Zhang, Danna; Wei Biaowu
作者单位：State University System of Florida; University of Central Florida; University of California System; University of California San Diego; University of Chicago
摘要：We establish an approximation theory for Pearson's chi-squared statistics in situations where the number of cells is large, by using a high-dimensional central limit theorem for quadratic forms of random vectors. Our high-dimensional central limit theorem is proved under Lyapunov-type conditions that involve a delicate interplay between the dimension, the sample size, and the moment conditions. We propose a modified chi-squared statistic and introduce an adjusted degrees of freedom. A simulati...
-
作者：Stanghellini, Elena; Doretti, Marco
作者单位：University of Perugia; University of Perugia
摘要：We derive the exact formula linking the parameters of marginal and conditional logistic regression models with binary mediators when no conditional independence assumptions can be made. The formula has the appealing property of being the sum of terms that vanish whenever parameters of the conditional models vanish, thereby recovering well-known results as particular cases. It also permits the disentangling of direct and indirect effects as well as quantifying the distortion induced by the omis...
-
作者：Cui, Y.; Hannig, J.
作者单位：University of Pennsylvania; University of North Carolina; University of North Carolina Chapel Hill
摘要：Since the introduction of fiducial inference by Fisher in the 1930s, its application has been largely confined to relatively simple, parametric problems. In this paper, we present what might be the first time fiducial inference is systematically applied to estimation of a nonparametric survival function under right censoring. We find that the resulting fiducial distribution gives rise to surprisingly good statistical procedures applicable to both one-sample and two-sample problems. In particul...
-
作者：Kundu, Prosenjit; Tang, Runlong; Chatterjee, Nilanjan
作者单位：Johns Hopkins University; Johns Hopkins Bloomberg School of Public Health
摘要：Meta-analysis is widely popular for synthesizing information on common parameters of interest across multiple studies because of its logistical convenience and statistical efficiency. We develop a generalized meta-analysis approach to combining information on multivariate regression parameters across multiple studies that have varying levels of covariate information. Using algebraic relationships among regression parameters in different dimensions, we specify a set of moment equations for esti...
-
作者：Alhorn, K.; Schorning, K.; Dette, H.
作者单位：Dortmund University of Technology; Ruhr University Bochum
摘要：We consider the problem of designing experiments for estimating a target parameter in regression analysis when there is uncertainty about the parametric form of the regression function. A newoptimality criterion is proposed that chooses the experimental design to minimize the asymptotic mean squared error of the frequentist model averaging estimate. Necessary conditions for the optimal solution of a locally and Bayesian optimal design problem are established. The results are illustrated in sev...
-
作者：Berrett, T. B.; Samworth, R. J.
作者单位：University of Cambridge
摘要：We propose a test of independence of two multivariate random vectors, given a sample from the underlying population. Our approach is based on the estimation of mutual information, whose decomposition into joint and marginal entropies facilitates the use of recently developed efficient entropy estimators derived from nearest neighbour distances. The proposed critical values may be obtained by simulation in the case where an approximation to one marginal is available or by permuting the data oth...
-
作者：Battey, H. S.
作者单位：Imperial College London
摘要：We develop a theory of covariance and concentration matrix estimation on any given or estimated sparsity scale when the matrix dimension is larger than the sample size. Nonstandard sparsity scales are justified when such matrices are nuisance parameters, distinct from interest parameters, which should always have a direct subject-matter interpretation. The matrix logarithmic and inverse scales are studied as special cases, with the corollary that a constrained optimization-based approach is un...
-
作者：Taraldsen, G.; Lindqvist, B. H.
作者单位：Norwegian University of Science & Technology (NTNU)
-
作者：Lee, A.; Tiberi, S.; Zanella, G.
作者单位：University of Bristol; University of Zurich; University of Zurich; Swiss Institute of Bioinformatics; Bocconi University; Bocconi University
摘要：We consider the problem of approximating the product of n expectations with respect to a common probability distribution mu. Such products routinely arise in statistics as values of the likelihood in latent variable models. Motivated by pseudo-marginal Markov chain Monte Carlo schemes, we focus on unbiased estimators of such products. The standard approach is to sample N particles from mu and assign each particle to one of the expectations; this is wasteful and typically requires the number of...
-
作者：Liu, Yang; Sun, Wei; Reiner, Alexander P.; Kooperberg, Charles; He, Qianchuan
作者单位：University System of Ohio; Wright State University Dayton; Fred Hutchinson Cancer Center
摘要：Genetic pathway analysis has become an important tool for investigating the association between a group of genetic variants and traits. With dense genotyping and extensive imputation, the number of genetic variants in biological pathways has increased considerably and sometimes exceeds the sample size n. Conducting genetic pathway analysis and statistical inference in such settings is challenging. We introduce an approach that can handle pathways whose dimension p could be greater than n. Our ...
